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A316903
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Heinz numbers of aperiodic integer partitions whose reciprocal sum is the reciprocal of an integer.
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0
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 65, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 147, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 195, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257
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OFFSET
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1,1
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COMMENTS
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The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
A partition is aperiodic if its multiplicities are relatively prime.
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LINKS
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MATHEMATICA
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Select[Range[2, 1000], And[GCD@@FactorInteger[#][[All, 2]]==1, IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]]]&]
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CROSSREFS
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Cf. A000837, A002966, A051908, A058360, A100953, A296150, A316854, A316855, A316856, A316857, A316888-A316904.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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